Exactly Solvable Stochastic Processes for Traffic Modelling

We analyze different available methods in the study of the exactly solvable stochastic models and their application to construction and modeling the road traffc with acceleration/deceleration dynamics.

[1]  Stefan Grosskinsky Warwick,et al.  Interacting Particle Systems , 2016 .

[2]  A. Schadschneider,et al.  Metastable states in cellular automata for traffic flow , 1998, cond-mat/9804170.

[3]  R Kunzig,et al.  THE PHYSICS OF ... TRAFFIC , 1999 .

[4]  Luigi Cantini,et al.  Algebraic Bethe ansatz for the two species ASEP with different hopping rates , 2007, 0710.4083.

[5]  Giuseppe Mussardo,et al.  Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics , 2009 .

[6]  Dirk Helbing,et al.  Criticism of three-phase traffic theory , 2009 .

[7]  Nagel,et al.  Discrete stochastic models for traffic flow. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  R. Baxter,et al.  The inversion relation method for some two-dimensional exactly solved models in lattice statistics , 1982 .

[9]  W. Coffey,et al.  Diffusion and Reactions in Fractals and Disordered Systems , 2002 .

[10]  Y. Sugiyama,et al.  Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam , 2008 .

[11]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[12]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[13]  Haye Hinrichsen,et al.  ON MATRIX PRODUCT GROUND STATES FOR REACTION-DIFFUSION MODELS , 1996 .

[14]  Cyril Furtlehner,et al.  A Queueing Theory Approach for a Multi-Speed Exclusion Process , 2011, 1109.1756.

[15]  Paczuski,et al.  Emergent traffic jams. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[17]  G. Mil’shtein,et al.  Interaction of Markov Processes , 1972 .

[18]  D. Janzing,et al.  A single-shot measurement of the energy of product states in a translation invariant spin chain can replace any quantum computation , 2007, 0710.1615.

[19]  S. Havlin,et al.  Diffusion and Reactions in Fractals and Disordered Systems , 2000 .

[20]  B. Derrida,et al.  Exact solution of a 1d asymmetric exclusion model using a matrix formulation , 1993 .